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mmend98

  • one year ago

The function f(x) = 4(4)x represents the growth of a fly population every year in a remote swamp. Jackie wants to manipulate the formula to an equivalent form that calculates three times a year, not just once a year. Which function is correct for Jackie's purpose, and what is the new growth rate? (5 points) f(x) = 4(4)x; growth rate 400% f(x) = 4(4)3x, growth rate 4% f(x) = 4(1.59)3x; growth rate 59% f(x) = 4(1.59)x; growth rate 4%

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  1. thomas5267
    • one year ago
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    What is f(x) equal to? What is 4(4)x?

  2. mmend98
    • one year ago
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    I think it would be B.

  3. mmend98
    • one year ago
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    they are exponential as well the answers sorry for the typo

  4. ganeshie8
    • one year ago
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    rearrange the exponent as \(\frac{3x}{3}\) and simplify : \[\large{\begin{align}f(x)=4(4)^x &= 4(4)^{\frac{3x}{3}}\\~\\ &= 4(4^{\frac{1}{3}})^{3x}\\~\\ &= ? \end{align}}\]

  5. mmend98
    • one year ago
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    ok

  6. ganeshie8
    • one year ago
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    use ur calculator to work \(\large 4^{\frac{1}{3}}\)

  7. mmend98
    • one year ago
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    16.3

  8. ganeshie8
    • one year ago
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    nope, try again

  9. ganeshie8
    • one year ago
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    wolf says \(\approx 1.59\) http://www.wolframalpha.com/input/?i=4%5E%281%2F3%29

  10. mmend98
    • one year ago
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    ah

  11. mmend98
    • one year ago
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    So the answer would be D?

  12. mmend98
    • one year ago
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    or C.

  13. mmend98
    • one year ago
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    c would be the answer

  14. ganeshie8
    • one year ago
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    right, one of them how do we pin down which one it is

  15. mmend98
    • one year ago
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    it is c?

  16. ganeshie8
    • one year ago
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    how do you know

  17. mmend98
    • one year ago
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    because it is the same but manipulatd as the original equation

  18. ganeshie8
    • one year ago
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    rearrange the exponent as \(\frac{3x}{3}\) and simplify : \[\large{\begin{align}f(x)=4(4)^x &= 4(4)^{\frac{3x}{3}}\\~\\ &= 4(4^{\frac{1}{3}})^{3x}\\~\\ &= 4(1.\color{red}{59})^{3x}\\~\\ \end{align}}\] that red part gives you the growth rate

  19. mmend98
    • one year ago
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    oh ok.

  20. ganeshie8
    • one year ago
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    the fly population grows at a rate of \(59\%\) per quarter

  21. mmend98
    • one year ago
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    we know c is the anser because 59 percent is the growht rate

  22. mmend98
    • one year ago
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    ?

  23. ganeshie8
    • one year ago
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    yes ?

  24. mmend98
    • one year ago
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    yes

  25. IrishBoy123
    • one year ago
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    .

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